Method and apparatus for device linearization

ABSTRACT

Various embodiments are disclosed of apparatuses and methods for linearization. A linearized signal can control, for example, a microelectromechanical device, a microelectromechanical device, and/or a device controlling a modulated intensity of electromagnetic energy. Some embodiments include linearization functions such as a logarithm or x/(a+x).

CROSS REFERENCE TO RELATED APPLICATION

[0001] This application is a continuation-in-part of and claims the benefit of priority from the U.S. application Ser. No. 09/548,788, filed Apr. 13, 2000, which application is fully incorporated herein by reference.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The field relates to linearization of a response to a signal. More particularly, the field relates to linearizing a response, such as an intensity from a light-modulating device, to an input signal.

[0004] 2. Description of the Related Art

[0005] Many systems, in response to a linear input, exhibit a highly nonlinear output response. Such a nonlinear response can complicate the control of the system output. Therefore, what is needed is a way to linearize a system output relative to a system input.

SUMMARY OF THE INVENTION

[0006] Some embodiments can comprise two relatively constant signal references coupled to each other by two or more signal components coupled in series. The first signal component can include a variable signal component controlled by an external input signal. The second signal component can include a relatively fixed signal component. The output node can include a node coupling the variable signal component and the relatively fixed signal component. The output node can provide an output signal controlling, for example, a microelectromechanical device, and/or a device controlling a modulated intensity of electromagnetic energy.

[0007] Some embodiments can comprise an input node coupled to an output node via an intermediate circuit. The intermediate circuit can comprise a logarithm circuit and/or a lookup table. The output node can provide an output signal controlling, for example, a microelectromechanical device, and/or a device controlling a modulated intensity of electromagnetic energy.

[0008] Some embodiments comprise receiving a first signal determining a first quantity responsive to the first signal, generating a second signal determined at least by a lookup table, and sending the second signal to, for example, a microelectromechanical device adapted to respond to the second signal, and/or a device adapted to respond to the second signal. The device can control a modulated intensity of electromagnetic energy.

[0009] Some embodiments can comprise receiving a first signal, determining a first quantity responsive to the first signal, generating a second signal determined at least by a quotient, and sending the second signal to, for example, a microelectromechanical device adapted to respond to the second signal, and/or a device adapted to respond to the second signal. The quotient can comprise the first quantity divided by a sum, and the sum can comprise an addition of the first quantity and a second quantity. The device can control a modulated intensity of electromagnetic energy.

[0010] Some embodiments can comprise receiving a first input, and, responsive to the first input, sending a second input to an element, for example, a microelectromechanical device, and/or a device controlling a modulated intensity of electromagnetic energy. The second input can substantially linearize the first input, over a range of the first input, relative to an output of the element. The output of the element can be substantially proportional to the first input over the range of the first input.

[0011] Some embodiments can comprise receiving a first input, processing the first input through at least one circuit to produce a second input, and sending the second input to a device controlling a modulated intensity of electromagnetic energy. The modulated intensity can be substantially proportional to the first input over a range of the first input.

[0012] Some embodiments can comprise receiving a first signal, determining a first quantity responsive to the first signal, generating a second signal determined at least by a logarithm of at least the first quantity, and sending the second signal to, for example, a microelectromechanical device adapted to respond to the second signal, and/or a device adapted to respond to the second signal. The device can control a modulated intensity of electromagnetic energy.

BRIEF DESCRIPTION OF THE FIGURES

[0013]FIG. 1 shows a graph of a nonlinear transfer function.

[0014]FIG. 2 shows an example of a linearizing transfer function for the nonlinear transfer function of FIG. 1.

[0015]FIG. 3 shows a graph of a curve resulting from inserting, before a nonlinear transfer function, a linearizing transfer function including a logarithmic function.

[0016]FIG. 4 shows a graph a curve resulting from inserting, before a nonlinear transfer function, a linearizing transfer function including a function x/(a+x).

[0017]FIG. 5 shows a linearization apparatus.

[0018]FIG. 6 shows another linearization apparatus.

DETAILED DESCRIPTION

[0019] Some embodiments are related to linearization of the transfer function of an element, for example, an electrically actuated membrane. In some applications, the membrane can be used as part of a microelectromechanical grating. The grating can act as a lightvalve, or variable optical attenuator (VOA).

[0020] In one embodiment, a membrane has openings suspended above a substrate covering about 50% of the overall substrate area. Both the top surface of the membrane and the exposed surface of the substrate can be optically reflective and/or transmissive. Light reflected and/or transmitted from the membrane and light reflected and/or transmitted from the substrate can have a certain phase difference depending on the distance between the membrane and the substrate. Depending on the phase difference, the two sources of reflected and/or transmitted light interfere either constructively or destructively, leading to possible attenuation of the reflected and/or transmitted light. The extent of attenuation can therefore be controlled by adjusting the position of the membrane.

[0021] In one embodiment, movement of the membrane can be accomplished electrostatically. A top surface of the membrane can be metallized to form a top electrode, and the substrate can be made electrically conductive to form a bottom electrode. A voltage applied across the two electrodes can cause the membrane to be attracted towards the substrate. The amount of deflection can depend on the amplitude of the voltage applied.

[0022] For any given membrane deflection, one can calculate a voltage required to produce that deflection. The following is one example of a relationship between the voltage and the deflection, where σ is the (tensile) stress of the membrane film, t_(membrane) is the thickness of the membrane, ε_(r) is the relative dielectric constant of the membrane material, ε_(air) is the relative dielectric constant of air (about 1), ε₀ is the permittivity of free space, D is the distance from the bottom of the membrane to the substrate, ΔD is the deflection of the membrane, and L is the length of the membrane: $V_{applied} = \sqrt{\frac{\left( {\frac{t_{membrane}}{ɛ_{r}} + \frac{D}{ɛ_{air}} - {\Delta \quad D}} \right)^{2}}{L^{2}ɛ_{0}}}$

[0023] For any given membrane deflection, one can calculate the expected optical attenuation resulting from that deflection. The following is one example of a relationship between the optical attenuation and the deflection, where I_(reflected) is the reflected light intensity, ΔD is the deflection of the membrane, and λ is the wavelength of the light: $I_{reflected} = {\cos^{2}\left( \frac{2\pi \quad \Delta \quad D}{\lambda} \right)}$

[0024]FIG. 1 shows a graph of a transfer function 100 of attenuation plotted versus voltage, using the above formulas. One embodiment linearizes the transfer function of FIG. 1.

[0025] The transfer function 100 can be very nonlinear. In one example of the transfer function 100, the attenuation can vary very slowly with voltage at low voltages, but can change very quickly at high voltages. Nonlinear behavior can create difficulties in control of the element. Therefore, it can be advantageous to linearize the transfer function 100.

[0026] In some embodiments, linearization can be accomplished by inserting an intermediate transfer function 200, somewhere before the element. The transfer function 200 can have largely opposite characteristics to transfer function 100. For example, transfer function 200 can initially vary quickly with voltage, then vary slowly. FIG. 2 shows one example of a transfer function 200. Various embodiments of the transfer function 200 can include, for example, a logarithmic function, and/or a function x/(a+x), where a is some constant and x is some variable.

[0027]FIG. 3 shows a graph of curve 300 resulting from inserting transfer function 200 before transfer function 100 for an embodiment where transfer function 200 includes a logarithmic function. FIG. 4 shows a graph of curve 400 for a case where transfer function 200 includes a function x/(a+x). FIG. 4 also shows a graph of curve 410 demonstrating ideal linearization. In one embodiment, the non-linearity can be within 1%, within the range of 2.5 dB to 17.5 dB. Other embodiments can demonstrate other nonlinearities and/or other ranges.

[0028] Some embodiments can comprise receiving a first signal, determining a first quantity responsive to the first signal, generating a second signal determined at least by a quotient, and sending the second signal to an element, for example, a membrane adapted to respond to the second signal, a microelectromechanical device adapted to respond to the second signal, and/or a device adapted to respond to the second signal. The quotient can comprise the first quantity divided by a sum, and the sum can comprise an addition of the first quantity and a second quantity. The first quantity can comprise a variable resistance determined at least by the first signal and/or a variable reactance determined at least by the first signal. The variable reactance can comprise at least one inductance and/or at least one capacitance. The second quantity can comprise a constant. The constant can comprise a resistance, for example in a plurality of resistances. The constant can comprise at least one reactance. The reactance can comprise at least one inductance and/or at least one capacitance. A response of the element can be made substantially proportional to the first signal over a range of the first signal, for example, due at least to the second signal. The device can control a reflected and/or transmitted intensity of electromagnetic energy. At least part of the electromagnetic energy can reside within, for example, in the optical C-band, or the optical L-band, or the both the L-band and the C-band from about 1530 nm to about 1610 nm.

[0029] Some embodiments can comprise receiving a first input, processing the first input through at least one look up table to produce a second input, and sending the second input to a device controlling a modulated intensity of electromagnetic energy. At least part of the electromagnetic energy can reside within, for example, in the optical C-band, or the optical L-band, or the both the L-band and the C-band from about 1530 nm to about 1610 nm. The modulated intensity can be made substantially proportional to the first input over a range of the first input. Other embodiments can further comprise receiving the second input at the device, and controlling the modulated intensity of the device responsive to the second input.

[0030] Some embodiments can comprise receiving a first signal, determining a first quantity responsive to the first signal, generating a second signal determined at least by a logarithm of at least the first quantity, and sending the second signal to an element, for example, a membrane adapted to respond to the second signal, a microelectromechanical device adapted to respond to the second signal, and/or a device adapted to respond to the second signal. The device can control a modulated intensity of electromagnetic energy. At least part of the electromagnetic energy can reside within, for example, in the optical C-band, or the optical L-band, or the both the L-band and the C-band from about 1530 nm to about 1610 nm. A response of the element can be made substantially proportional to the first signal over a range of the first signal, for example due at least to the second signal.

[0031]FIG. 5 shows some embodiments 500 of a linearization apparatus. Some embodiments can comprise a first signal reference 510, a constant signal component 520, an output node 530, a variable signal component 540, and a second signal reference 550. The constant signal component 520 can be coupled to the first signal reference 510. The first signal reference 510 can comprise a variable input voltage or a constant voltage. The constant voltage can comprise a ground or some other voltage. The output node 530 can be coupled to the constant signal component 520 The constant signal component 520 can comprise a resistor, for example in a plurality of resistors. The constant signal component 520 and/or the variable signal component 540 can comprise a device having a reactance. The reactance can comprise at least one inductance and/or at least one capacitance. The output node 530 can provide an output signal controlling an element, for example, a membrane, a microelectromechanical device, and/or a device controlling a modulated intensity of electromagnetic energy. The apparatuses 500 can further comprise the element. The element can be coupled to the output node 530 The variable signal component 540 can be coupled to the output node 530 and to an input. The variable signal component 540 can comprise at least one variable resistor. At least one of the constant signal component 520 and the variable signal component 540 can comprise at least one of a current, a voltage, and a resistance. The constant signal component 520 and the variable signal component 540 can be coupled in series and/or in parallel. At least one look up table can comprise at least one of the constant signal component 520 and the variable signal component 540. The second signal reference 550 can be coupled to the variable signal component 540. A response of the element to the output signal can be substantially proportional to an input signal received at the input. The second signal reference 550 can comprise a constant voltage. The constant voltage can comprise a ground or some other voltage.

[0032] One embodiment of the apparatus includes a variable resistive divider. The divider can include a manually adjustable potentiometer, and/or an electronically controlled digital potentiometer. Some embodiments include a variable resistor which, when adjusted to its maximum resistance, is 17-25 times that of the fixed resistor. Other embodiments can use the 17-25 ratio of maximum magnitudes for other device combinations. The maximum magnitude can be a physical or software maximum of a device or an arbitrary limit that remains within a small range of a device.

[0033]FIG. 6 shows other embodiments 600 of a linearization apparatus. Some embodiments comprise a plurality of resistors 620 coupled in parallel, and a variable resistor 640. In one embodiment, the plurality of resistors 620 and the variable resistor 640 can be included in a quad-package digital potentiometer. The variable resistor 640 can be used as the variable part of the resistive divider. Another variable resistor 645 can also be used as another variable part of the resistive divider. The plurality of resistors 620 coupled in parallel can be programmed upon power-up.

[0034] Embodiments with a multi-resistor package include devices that are well-matched, such as in terms of fabrication quality and/or thermally during operation. Other embodiments include one or more of the devices in different packages. Embodiments with multiple devices for one or both of the constant signal component 520 and the variable signal component 540 can adjust an aggregate value in smaller increments. For example, if multiple resistors are in parallel, adjusting only one of the resistors results in a smaller adjustment.

[0035] Some embodiments include multiple devices for one or both of the constant signal component 520 and the variable signal component 540 to decrease temperature dependence. For example, some resistors with a resolution of a number steps, (e.g. the 4-in-a-package AD 8403 from Analog Devices, in which each resistor has a 256-step resolution) can exhibit a relatively high temperature coefficient of resistance at “small” counts (e.g., less than 16). By using a 2-up parallel combination for the constant signal component 520, and assuming a ratio of about 20 between the maximum resistance of the variable resistor in the variable signal component 540 and the resistance of the 2-up parallel combination in the constant signal component 520, each of the parallel resistors can be programmed to a value of (256/20)*2=25 or 26 counts, greater than 16 counts.

[0036] Although some embodiments of linearization assume only the variable signal component 540 to be variable, one or more devices of the constant signal component 520 can also be varied, for example for fine-adjustment.

[0037] Other embodiments include other configurations of resistors to implement the transfer function 200 Some configurations can give extra stability or precision depending on the components.

[0038] Other embodiments can include a capacitor in series with a resistor, combined with a V-f (voltage-frequency) converter and a RMS (root-mean-square) converter to provide similar functionality.

[0039] Constant values can be constant per use of an apparatus or method or for some duration smaller or longer than a use.

[0040] Other embodiments can further comprise receiving the second signal at the element, and controlling the element responsive to the second signal. At least one of the first quantity and the second quantity can comprise at least one of a current and a voltage. In some embodiments, at least one look up table can comprise at least one of the quotient and the first quantity.

[0041] Various embodiments can comprise parts coupled together physically and/or functionally. The various embodiments of the structures and methods that are described above are illustrative only and do not limit the scope to the particular embodiments described. For example, in view of this disclosure, those skilled in the art can define other electrical or optical or mechanical devices. The following claims cover such alternatives. 

What is claimed is:
 1. An apparatus for linearization, comprising: an input node adapted to receive an input signal to control a microelectromechanical device; a system responsive to the input signal, wherein the system is adapted to generate an output signal determined at least by a quotient, and the quotient comprises a relatively variable quantity divided by a sum, and the sum comprises an addition of the relatively variable quantity and a relatively constant quantity, and the relatively variable quantity is determined at least in part by the input signal; and an output node adapted to provide the output signal to control the microelectromechanical device.
 2. The apparatus of claim 1, further comprising: the microelectromechanical device coupled to the output node.
 3. The apparatus of claim 1, wherein a response of the microelectromechanical device to the output signal is substantially proportional to the input signal received at the input node.
 4. The apparatus of claim 1, wherein the microelectromechanical device comprises a suspended structure.
 5. The apparatus of claim 1, wherein the microelectromechanical device comprises an optical structure.
 6. The apparatus of claim 1, wherein the microelectromechanical device controls a modulated intensity of electromagnetic energy.
 7. The apparatus of claim 6, wherein at least part of the electromagnetic energy is within a wavelength range of about 1530 nm to about 1610 nm.
 8. The apparatus of claim 1, wherein the system comprises: at least one look up table comprising values of the input signal and the output signal.
 9. The apparatus of claim 1, wherein the system further comprises: a first signal reference; a second signal reference; a constant signal component coupled to the first signal reference; and a variable signal component coupled to the output node and to the second signal reference.
 10. The apparatus of claim 9, wherein the first signal reference comprises a variable input voltage.
 11. The apparatus of claim 9, wherein the first signal reference comprises a constant voltage.
 12. The apparatus of claim 9, wherein the constant signal component comprises a resistor.
 13. The apparatus of claim 9, wherein the constant signal component comprises a plurality of resistors.
 14. The apparatus of claim 9, wherein the variable signal component comprises at least one variable resistor.
 15. The apparatus of claim 9, wherein the second signal reference comprises a constant voltage.
 16. The apparatus of claim 9, wherein at least one of the constant signal component and the variable signal component comprises at least one of a current and a voltage.
 17. The apparatus of claim 9, wherein the variable signal component comprises a device having a reactance.
 18. The apparatus of claim 17, wherein the reactance comprises at least one inductance.
 19. The apparatus of claim 17, wherein the reactance comprises at least one capacitance.
 20. The apparatus of claim 9, wherein the constant signal component and the variable signal component are coupled in series.
 21. The apparatus of claim 9, wherein a maximum magnitude of the variable signal component is greater than a magnitude of the constant signal component by a factor, the factor being in a range of about 17 to about
 25. 22. An apparatus for linearization, comprising: an input node adapted to receive an input signal to control a microelectromechanical device; a system responsive to the input signal, wherein the system is adapted to generate an output signal determined at least by a logarithm of a relatively variable quantity, and the relatively variable quantity is determined at least in part by the input signal; and an output node adapted to provide the output signal to control the microelectromechanical device.
 23. The apparatus of claim 22, further comprising: the microelectromechanical device coupled to the output node.
 24. The apparatus of claim 22, wherein a response of the microelectromechanical device to the output signal is substantially proportional to the input signal received at the input node.
 25. The apparatus of claim 22, wherein the microelectromechanical device comprises a suspended structure.
 26. The apparatus of claim 22, wherein the microelectromechanical device comprises an optical structure.
 27. The apparatus of claim 22, wherein the microelectromechanical device controls a modulated intensity of electromagnetic energy.
 28. The apparatus of claim 27, wherein at least part of the electromagnetic energy is within a wavelength range of about 1530 nm to about 1610 nm.
 29. The apparatus of claim 22, wherein the system comprises: at least one look up table comprising values of the input signal and the output signal.
 30. An apparatus for linearization, comprising: an input node adapted to receive an input signal to control a microelectromechanical device; a system responsive to the input signal, wherein the system is adapted to generate an output signal determined at least by one or more look up tables, and the one or more look up tables comprising values of the input signal and the output signal; and an output node adapted to provide the output signal to control the microelectromechanical device.
 31. The apparatus of claim 30, further comprising: the microelectromechanical device coupled to the output node.
 32. The apparatus of claim 30, wherein a response of the microelectromechanical device to the output signal is substantially proportional to the input signal received at the input node.
 33. The apparatus of claim 30, wherein the microelectromechanical device comprises a suspended structure.
 34. The apparatus of claim 30, wherein the microelectromechanical device comprises an optical structure.
 35. The apparatus of claim 30, wherein the microelectromechanical device controls a modulated intensity of electromagnetic energy.
 36. The apparatus of claim 35, wherein at least part of the electromagnetic energy is within a wavelength range of about 1530 nm to about 1610 mn.
 37. A method of linearization, comprising: receiving a first signal; determining a first quantity responsive to the first signal; generating a second signal determined at least by a quotient, wherein the quotient comprises the first quantity divided by a sum, and the sum comprises an addition of the first quantity and a second quantity; and sending the second signal to a microelectromechanical device adapted to respond to the second signal.
 38. The method of claim 37, wherein a response of the microelectromechanical device is substantially proportional to the first signal over a range of the first signal.
 39. The method of claim 37, wherein due at least to the second signal, a response of the microelectromechanical device is substantially proportional to the first signal over a range of the first signal.
 40. The method of claim 37, wherein the second quantity comprises a constant.
 41. The method of claim 40, wherein the constant comprises a resistance.
 42. The method of claim 40, wherein the constant comprises a plurality of resistances.
 43. The method of claim 37, wherein the first quantity comprises a variable resistance determined at least by the first signal.
 44. The method of claim 37, wherein the first quantity comprises a variable reactance determined at least by the first signal.
 45. The method of claim 44, wherein the variable reactance comprises at least one inductance.
 46. The method of claim 44, wherein the variable reactance comprises at least one capacitance.
 47. The method of claim 37, further comprising: receiving the second signal at the microelectromechanical device; and controlling the microelectromechanical device responsive to the second signal.
 48. The method of claim 37, wherein at least one of the first quantity and the second quantity comprises at least one of a current and a voltage.
 49. The method of claim 37, wherein at least one look up table comprises at least one of the quotient and the first quantity.
 50. The method of claim 37, wherein a maximum magnitude of the first quantity is greater than a magnitude of the second quantity by a factor, the factor being in range of about 17 to
 25. 51. A method of linearization, comprising: receiving a first signal; determining a first quantity responsive to the first signal; generating a second signal determined at least by a quotient, wherein the quotient comprises the first quantity divided by a sum, and the sum comprises an addition of the first quantity and a second quantity; and sending the second signal to a device adapted to respond to the second signal, wherein the device controls a modulated intensity of electromagnetic energy.
 52. The method of claim 51, wherein a response of the device is substantially proportional to the first signal over a range of the first signal.
 53. The method of claim 51, wherein due at least to the second signal, a response of the device is substantially proportional to the first signal over a range of the first signal.
 54. The method of claim 51 wherein the second quantity comprises a constant.
 55. The method of claim 54, wherein the constant comprises a resistance.
 56. The method of claim 54, wherein the constant comprises a plurality of resistances.
 57. The method of claim 51, wherein the first quantity comprises a variable resistance determined at least by the first signal.
 58. The method of claim 51, wherein the first quantity comprises a variable reactance determined at least by the first signal.
 59. The method of claim 58, wherein the variable reactance comprises at least one inductance.
 60. The method of claim 58, wherein the variable reactance comprises at least one capacitance.
 61. The method of claim 51, further comprising: receiving the second signal at the device; and controlling the device responsive to the second signal.
 62. The method of claim 51, wherein at least one of the first quantity and the second quantity comprises at least one of a current and a voltage.
 63. The method of claim 51, wherein at least one look up table comprises at least one of the quotient and the first quantity.
 64. The method of claim 51, wherein at least part of the electromagnetic energy is within a wavelength range of about 1530 nm to about 1610 nm.
 65. The method of claim 51, wherein a maximum magnitude of the first quantity is greater than a magnitude of the second quantity by a factor, the factor being in a range of about 17 to
 25. 66. A method of linearization, comprising: receiving a first input; responsive to the first input, sending a second input to a microelectromechanical device, wherein the second input substantially linearizes the first input, over a range of the first input, relative to an output of the microelectromechanical device, such that the output of the microelectromechanical device is substantially proportional to the first input over the range of the first input.
 67. The method of claim 66, further comprising: receiving the second input at the microelectromechanical device; and determining the output of the microelectromechanical device responsive to the second input.
 68. A method of linearization, comprising: receiving a first signal; determining a first quantity responsive to the first signal; generating a second signal determined at least by a logarithm of at least the first quantity; and sending the second signal to a microelectromechanical device adapted to respond to the second signal.
 69. The method of claim 68, wherein a response of the microelectromechanical device is substantially proportional to the first signal over a range of the first signal.
 70. The method of claim 68, wherein due at least to the second signal, a response of the microelectromechanical device is substantially proportional to the first signal over a range of the first signal.
 71. The method of claim 68, further comprising: receiving the second signal at the microelectromechanical device; and controlling the microelectromechanical device responsive to the second signal.
 72. The method of claim 68, wherein at least one look up table comprises at least one of the logarithm and the first quantity.
 73. A method of linearization, comprising: receiving a first signal; determining a first quantity responsive to the first signal; generating a second signal determined at least by a logarithm of the first quantity; and sending the second signal to a device adapted to respond to the second signal, wherein the device controls a modulated intensity of electromagnetic energy.
 74. The method of claim 73, wherein a response of the device is substantially proportional to the first signal over a range of the first signal.
 75. The method of claim 73, wherein due at least to the second signal, a response of the device is substantially proportional to the first signal over a range of the first signal.
 76. The method of claim 73, further comprising: receiving the second signal at the device; and controlling the device responsive to the second signal.
 77. The method of claim 73, wherein at least one look up table comprises at least one of the logarithm and the first quantity.
 78. The method of claim 73, wherein at least part of the electromagnetic energy is within a wavelength range of about 1530 nm to about 1610 nm.
 79. A method of linearization, comprising: receiving a first signal; generating a second signal determined at least by a look up table comprising a value of a second signal corresponding to a value of the first signal; and sending the second signal to a microelectromechanical device adapted to respond to the second signal.
 80. The method of claim 79, wherein a response of the microelectromechanical device is substantially proportional to the first signal over a range of the first signal.
 81. The method of claim 79, wherein due at least to the second signal, a response of the microelectromechanical device is substantially proportional to the first signal over a range of the first signal.
 82. The method of claim 79, further comprising: receiving the second signal at the microelectromechanical device; and controlling the microelectromechanical device responsive to the second signal.
 83. A method of linearization, comprising: receiving a first signal; determining a first quantity responsive to the first signal; generating a second signal determined at least by a look up table comprising values of the first signal and values of the signal; and sending the second signal to a device adapted to respond to the second signal, wherein the device controls a modulated intensity of electromagnetic energy.
 84. The method of claim 83, wherein a response of the device is substantially proportional to the first signal over a range of the first signal.
 85. The method of claim 83, wherein due at least to the second signal, a response of the device is substantially proportional to the first signal over a range of the first signal.
 86. The method of claim 83, further comprising: receiving the second signal at the device; and controlling the device responsive to the second signal.
 87. The method of claim 83, wherein at least part of the electromagnetic energy is within a wavelength range of about 1530 nm to about 1610 nm. 